TY - JOUR
T1 - Traveling wave solutions using the variational method and the tanh method for nonlinear coupled equations
AU - Al-Khaled, Kamel
AU - Al-Refai, Mohammed
AU - Alawneh, Ameen
PY - 2008/8/1
Y1 - 2008/8/1
N2 - This paper applied both the tanh and the He's variational iteration methods for analytic study for the nonlinear coupled Kortewge-de Vries (shortly, KdV) equations. Compared with existing sophisticated approaches, the proposed methods gives more general exact traveling wave solutions without much extra effort. Finally, we present an application to shallow water equations using the two methods, the calculations demonstrate the effectiveness and convenience of the He's variational method for nonlinear coupled equations.
AB - This paper applied both the tanh and the He's variational iteration methods for analytic study for the nonlinear coupled Kortewge-de Vries (shortly, KdV) equations. Compared with existing sophisticated approaches, the proposed methods gives more general exact traveling wave solutions without much extra effort. Finally, we present an application to shallow water equations using the two methods, the calculations demonstrate the effectiveness and convenience of the He's variational method for nonlinear coupled equations.
KW - Coupled KdV equations
KW - Shallow water equations
KW - Traveling wave solutions
KW - Variational iteration method
KW - tanh method
UR - http://www.scopus.com/inward/record.url?scp=46749083042&partnerID=8YFLogxK
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U2 - 10.1016/j.amc.2008.02.009
DO - 10.1016/j.amc.2008.02.009
M3 - Article
AN - SCOPUS:46749083042
SN - 0096-3003
VL - 202
SP - 233
EP - 242
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
IS - 1
ER -